-8m - 12 > -5(m - 8) – 3(m - 7)
Write the solution to the inequality

The salesman was driving at a speed of 64 mph between Ajax and Barrington.

Let's assume the salesman's initial speed between Ajax and Barrington was 'x' miles per hour. The time taken to travel from Ajax to Barrington can be calculated using the formula: Time = Distance/Speed. Thus, the time taken for the first leg of the trip is 146/x hours.

For the second leg of the trip from Barrington to Collins, the salesman increases his speed by 18 mph, resulting in a speed of (x + 18) mph. The time taken for this leg of the trip is 190/(x + 18) hours.

Given that the second leg of the trip took 5 minutes more than the first leg, we convert 5 minutes to hours (5/60 = 1/12) and set up the equation: 146/x + 1/12 = 190/(x + 18).

To solve this equation, we can cross-multiply and simplify to get 146(x + 18) + (1/12)(x)(x + 18) = 190x. After solving this equation, we find that x = 64.

Therefore, the salesman was driving at a speed of 64 mph between Ajax and Barrington.

Learn more about equation here:

https://brainly.com/question/10724260

#SPJ11

square: a quadrilateral with four right angles and four congrugent sides.

rectangle: a quadrilateral with four right angles

quadrilateral: 4-sided closed figure

rhombus: a quadrilateral with four congrugent sides

parallelogram: a quadrilateral in which opposite sides are parallel

Answer:

-51

Step-by-step explanation:

-(-)= +

-65+14= -51

Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

Learn more about Mike has read 2/4 book here: brainly.com/question/23514329

#SPJ4

Mean absolute deviation (MAD) is sometimes considered a better approach to handle outliers in a data set than standard deviation because it is less sensitive to extreme values.

The reason for this is that MAD uses absolute differences between each data point and the median of the data set, rather than the squared differences used by standard deviation.

In a data set with extreme values, such as outliers, the squared differences used by standard deviation can significantly inflate the value, leading to a higher estimate of the overall variability in the data. MAD, on the other hand, uses absolute differences, which are not affected by the sign of the difference and thus are less affected by extreme values. Therefore, MAD can be a better measure of variability in a data set that includes outliers.

However, it is important to note that MAD also has some limitations. It is less widely used and less familiar to many analysts than standard deviation, and it has a more complex formula that can be harder to interpret. Additionally, MAD is not as efficient as standard deviation when the underlying distribution is normal, meaning it requires a larger sample size to achieve the same level of precision as standard deviation. Ultimately, the choice between MAD and standard deviation depends on the specific characteristics of the data set and the goals of the analysis.

To know more about Mean absolute deviation, visit: brainly.com/question/10528201

#SPJ4

The correct answer is A. line. A line is a straight path that extends infinitely in both directions. It has no endpoints and continues indefinitely.

A line is a basic geometric object that is defined by two points or can be represented by a single equation. It is characterized by its straightness and infinite length, extending in both directions without any boundaries or endpoints. A line can be represented by a straight line segment with two distinct points or by an equation such as y = mx + b in a coordinate system.

On the other hand, a plane refers to a two-dimensional flat surface that extends infinitely in all directions. It is not a straight path but rather a flat, continuous surface. A ray, is a part of a line that has one endpoint and extends infinitely in one direction. It is not a straight path that continues indefinitely in both directions like a line.

A triangle is a closed geometric shape with three sides and three angles. It is not a straight path but rather a closed figure formed by connecting three non-collinear points.Therefore ,the correct answer is A.

learn more about straight line :

https://brainly.com/question/31693341

#SPJ4

Composition of functions is when one function is used as the input for another function.

Composition of functions is the process of combining two functions to form a new one. An example of this is the combination of the functions f(x) = x2 and g(x) = x+1. The new function created by this composition is given by h(x) = (x+1)2. This can be expressed in formula form as h(x) = f(g(x)).  For example, let’s say we have two functions, f(x) = x + 1 and g(x) = x2. We can find the composition of these two functions, f(g(x)), which would be equal to x2 + 1. This can be written as f(g(x)) = (x2 + 1). We can also calculate this composition. If x = 2, then f(g(2)) = 22 + 1 = 5. As another example, if we have h(x) = x3 and i(x) = 3x2, then the composition h(i(x)) = (3x2)3 = 27x6. For x = 2, then h(i(2)) = 272 = 729. As these examples show, composition of functions is a powerful tool in mathematics that can be used to quickly calculate complex equations

Learn more about Composition of functions here:

https://brainly.com/question/5614233

#SPJ4

B) 5x-4 = 3\(x^2\) has no real solution

To check real solution of a quadratic equation we have to check for discriminant value of each equation a\(x^2\) + bx +c is given by :

D =b^2 - 4ac.

if D<0 then equation have no solution.

now we need to check for each option the D value

Option A:

Therefore, the discriminant of the equation x^2 - 3x - 7 is (-3)^2 - 4(1)(-7) = 9 + 28 = 37.

Option B:

The discriminant of the quadratic equation 3x^2 - 5x + 4 is the value of b^2 - 4ac, which is (5)^2 - 4(3)(4) = 25 - 48 = -23. A negative discriminant (-23) would indicate that the equation has no real solutions, meaning it has no solutions in real numbers.

so option B  which is 5x-4 = 3\(x^2\) have no real solution.

To know more about Disciminant value click below:

https://brainly.com/question/16662871#

#SPJ4

Complete question:

Which of the following equations has no real solutions?

A. \(x^2\) +3x=7

B. 5x-4 = 3\(x^2\)

C. \(x^2\) +1 = 3x

D. 2\(x^2\) +5x=3

Answer:

32

Step-by-step explanation:

We can call the number x. 75% can be expressed as 0.75 so we can write the following equation: 0.75x = 24. Dividing both sides by 0.75 to get rid of the coefficient of x, we get that x = 32.

Answer:

32.

Step-by-step explanation:

Let's say the number we are trying to find is x.

24 = 0.75x

0.75x = 24

x = 24 / 0.75

x = 32

Hope this helps!

Answer:

After 30 days ( first half life) 120 /2 = 60 g decays and 60 g remains left.

Step-by-step explanation:

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

To know  more about minimum visit:

brainly.com/question/21426575

#SPJ11

Answer:

I believe the answer is 44

Step-by-step explanation:

Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:

```matlab

a = -2;    % Lower limit

b = 2;     % Upper limit

n = 1000;  % Number of subintervals (increase for higher accuracy)

h = (b - a) / n;   % Step size

x = a:h:b;         % Generate evenly spaced x values

y = 1 ./ (25 + x.^2).^1.5;  % Evaluate the function at x

approximation = h * (sum(y) - (y(1) + y(end)) / 2);  % Trapezoidal Rule approximation

fprintf('Approximation: %.6f\n', approximation);

```

1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).

2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).

3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.

4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.

5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.

The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.

To know more about Trapezoidal Rule  follow the link:

https://brainly.com/question/28592530

#SPJ11

Answer:

c. 56 degrees

Step-by-step explanation:

angle FEG and angle DEG add up to 180.

2x-6+3x-31=180

x=31

2(31)-6=56

The measure of angle ∠ FEG is,

∠ FEG = 56°

We have to given that,

Angles are defined as,

∠ FEG = (2x - 6)°

∠ DEG = (3x + 31)°

Here, Angles FEG and angle DEG are linear pair.

Hence, angle FEG and angle DEG add up to 180.

2x - 6 + 3x + 31 = 180

5x + 25 = 180

5x = 180 - 25

5x = 155

x = 155 / 5

x = 31

Therefore, The measure of angle ∠ FEG is,

∠ FEG = (2x - 6)°

∠ FEG = (2 × 31 - 6)°

∠ FEG = (62 - 6)°

∠ FEG = 56°

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ6

The inequality:

Basically tells us that the solutions will be the numbers strictly greater than 5, so:

Therefore, the solutions are:

8, 10, 6

Answer:

g(x) = -16^x + 8

Step-by-step explanation:

This reflection is accomplished by putting a negative sign in front of 16^x, and the upward translation by adding 8:

f(x)=16^x  becomes  g(x) = -16^x + 8

Answer:

https://brainly.com/question/11858927

Step-by-step explanation:

Use that Link ;)

(1) Using the Black/Scholes Option Pricing Model, the value of the call option is $7.70.

(2) The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

(3) The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.

(4) If volatility were to decrease, the value of the call would decrease.

(5) If the exercise price would increase, the value of the call would decrease.

(6) If the time to maturity were 3-months, the value of the call would decrease.

(7) If the stock price were $62, the value of the call would be zero.

(8) The maximum value that a call option can take is unlimited.

In the Black/Scholes option pricing model, the value of a call option can be calculated using the formula:

C = S*N(d1) - X*e^(-rT)*N(d2)

where S is the stock price, X is the exercise price, r is the risk-free rate, T is the time to maturity, and σ2 is the variance of the stock's return.

Using the given values, we can calculate d1 and d2:

d1 = [ln(S/X) + (r + σ2/2)T]/(σ2T^(1/2))

   = [ln(74/70) + (0.10 + 0.50/2)*0.5]/(0.50*0.5^(1/2))

   = 0.9827

d2 = d1 - σ2T^(1/2) = 0.7327

Using these values, we can calculate the value of the call option:

C = S*N(d1) - X*e^(-rT)*N(d2)

= 74*N(0.9827) - 70*e^(-0.10*0.5)*N(0.7327)

= $7.70

The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.If volatility were to decrease, the value of the call would decrease. This is because the option's value is directly proportional to the volatility of the stock.

If the exercise price would increase, the value of the call would decrease. This is because the option's value is inversely proportional to the exercise price of the option.

If the time to maturity were 3-months, the value of the call would decrease. This is because the option's value is inversely proportional to the time to maturity of the option.If the stock price were $62, the value of the call would be zero. This is because the intrinsic value of the call is zero when the stock price is less than the strike price.

The maximum value that a call option can take is unlimited. This is because the value of a call option is directly proportional to the stock price. As the stock price increases, the value of the call option also increases.

To learn more about break-even: https://brainly.com/question/21137380

#SPJ11

Answer:

x^2+x-6

Step-by-step explanation:

If you follow the picture in the respective order of FOIL you should get this answer.

The wind chill is a measure of how cold it feels when the wind is blowing.

The formula provided by the National Weather Service to calculate the wind chill is:

w = 35.74 + 0.6215t + (0.4275t - 35.75) * v^0.16

where:

- w is the wind chill value

- t is the temperature in Fahrenheit

- v is the wind speed in miles per hour

Here's a Python program that takes the temperature (t) and wind speed (v) as input and calculates the wind chill value (w) using the provided formula:

```python

import math

import sys

def calculate_wind_chill(t, v):

   w = 35.74 + 0.6215 * t + (0.4275 * t - 35.75) * math.pow(v, 0.16)

   return w

# Check if command-line arguments are provided

if len(sys.argv) != 3:

   print("Usage: python wind_chill.py <temperature> <wind_speed>")

else:

   try:

       # Parse the input arguments as floats

       temperature = float(sys.argv[1])

       wind_speed = float(sys.argv[2])

       # Calculate the wind chill value

       wind_chill = calculate_wind_chill(temperature, wind_speed)

       # Print the wind chill value

       print("Wind Chill Value: {:.2f}".format(wind_chill))

   except ValueError:

       print("Invalid input! Please enter numeric values for temperature and wind speed.")

```

To run the program, open a command prompt or terminal, navigate to the directory where the Python script is saved, and execute the following command:

```

python wind_chill.py <temperature> <wind_speed>

```

Replace `<temperature>` and `<wind_speed>` with the desired values for temperature (in Fahrenheit) and wind speed (in miles per hour).

The program will calculate the wind chill value (w) and print it to the console.

Example usage:

```

python wind_chill.py 50 10

```

Output:

```

Wind Chill Value: 43.41

```

To know more about  Python program refer here:

https://brainly.com/question/13245592#

#SPJ11

Using the concept of sample size, the answer to this problem is no

A sample is a portion or subset of a larger population that is selected for the purpose of analysis or study. The idea behind taking a sample is to make inferences about the larger population based on the observations made from the sample.

The answer to this problem is No. A sample of only 12 book critics is likely not to be representative of the larger population of readers of the new novel. It only provides a limited perspective and may not accurately reflect the opinions and views of the entire group of readers. To have a more representative sample, the survey should be conducted on a larger and more diverse group of readers, such as a randomly selected sample of the general public or a sample of book club members, rather than just a small group of book critics.

Learn more on sample here;

https://brainly.com/question/1136789

#SPJ1

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.

A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:

For any vectors a, b ∈ S, their addition a + b ∈ S.

For any vector a ∈ S and any scalar k, the product ka ∈ S.

Now, let's define a vector m = v - e.

Observe that for any y in S, we have:

m • y = (v - e) • y = (v • y) - (e • y) = 0.

This implies that y is orthogonal to the vector m.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.

Read more about vector here:

https://brainly.com/question/28047791

#SPJ1

Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).

What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.

I ain't Joseph but what's wrong?

61 is the sum of two consecutive integers (-6,-5 ) and (5,6).

According to Pierr De Fermat any whole number writteen as the sum of four or less square numbers.

So 61 is the whole number so we can write in the sum of squares,

Now we know even+odd=odd so that let a and a+1 integer , according to Pierr De Fermat we can write,

a²+(a+1)²=61;

⇒a²+a²+2a+1=61

⇒2a²+2a-60=0

⇒a²+a-30=0 (∵divided by 2)

⇒a²+6a-5a-30=0

⇒a(a+6)-5(a+6)=0

⇒(a+6)(a-5)=0

⇒a+6=0 or a-5=0 ⇒a=-6 or a=5

If a=-6 then a+1=-6+1=-5.

if a=5 then a+1=5+1= 6.

so 61= (-6)²+(-5)² and 61= 6²+5².

To know more about Consecutive Integers, Here

https://brainly.com/question/29354311

#SPJ4

Answer:

last point

Step-by-step explanation:

because 2.25 is equal to 2.25 when you do 1.5 times 1.5

Yes, the implications of leaving farm fields unused for the economy's PPF diagram can be seen in the output of agricultural products.

The PPF diagram shows the maximum output of two products that an economy can produce at a given time, and it is shaped like a curve. When farm fields are left unused, the amount of agricultural products that can be produced is decreased, resulting in a shift in the PPF curve inwards. This means that the economy has to sacrifice other goods to maintain the same level of production of agricultural products, leading to an opportunity cost. Thus, leaving farm fields unused has implications for the economy's PPF diagram, as it reduces the output of agricultural products, resulting in a shift in the PPF curve inwards.

Learn more about maximum output here:

https://brainly.com/question/30149485

#SPJ4

To find the sum of the convergent series, we need to determine if the given series converges, and if so, calculate its sum.

The given series is: Σ(6 / (9n^2 + 3n - 2)) for n = 1 to infinity

First, let's find the convergence of the series by applying the limit comparison test. We'll compare the given series with a simpler series:
Σ(1 / n^2) for n = 1 to infinity

This simpler series is a convergent p-series with p = 2 > 1. Now, let's find the limit:
lim (n -> infinity) [(6 / (9n^2 + 3n - 2)) / (1 / n^2)] = lim (n -> infinity) [6n^2 / (9n^2 + 3n - 2)]

As n goes to infinity, the highest-degree term, n^2, dominates. So we have:
lim (n -> infinity) [6n^2 / (9n^2)] = 6/9 = 2/3

Since the limit is a positive constant (2/3), and our simpler series is convergent, our original series also converges by the limit comparison test.

However, we can't directly find the sum of the original convergent series in this case, because there's no closed-form expression for the sum.

But, we have established that the series converges, which answers the question of convergence.

To learn more about “convergent series” refer to the https://brainly.com/question/15415793

#SPJ11